Cosmology is making impressive progress and it is producing stringent bounds on the sum of the neutrino masses Sigma, a parameter of great importance for the current laboratory experiments. In this letter, we exploit the potential relevance of the analysis of Palanque-Delabrouille et al. [JCAP 02 (2015) 045] to the neutrinoless double beta decay (0 nu beta beta) search. This analysis indicates small values for the lightest neutrino mass, since the authors find Sigma < 84 meV at 1 sigma C.L., and provides a 1 sigma preference for the normal hierarchy. The allowed values for the Majorana effective mass, probed by 0 nu beta beta, turn out to be < 75 meV at 3 sigma C.L. and lower down to less than 20 meV at 1 sigma C.L.. If this indication is confirmed, the impact on the 0 nu beta beta experiments will be tremendous since the possibility of detecting a signal will be out of the reach of the next generation of experiments.
